Aerodynamic and aeroacoustic prediction tools are developed for rigid rotor blades in unsteady motion to provide insight into the aeroacoustics of vertical-axis wind turbine rotor blades. The aerodynamic component uses a subsonic unsteady inviscid panel method over the surface of the rotor blades to predict the unsteady pressure distribution over the surface, with vortex particles being shed from the blades to represent their freely-convecting wake. Using the velocity and pressure distributions over the rotor blades, the aeroacoustic component employs a non-penetrable version of Formulation 1C of the Ffowcs Williams-Hawkings equation to predict the noise from surface-based acoustic sources called thickness and loading noise. The prediction tools are compared to accepted results for fundamental test cases and vertical-axis wind turbines before being used to investigate the aerodynamics and acoustic noise of vertical-axis wind turbine rotors. Investigations into the effects of the blade geometry, the geometric scale of the rotor, the number of rotor blades, and the tip speed ratio of the rotor on the acoustic field are presented. The acoustic results are expected to under-predict the total acoustic noise of vertical-axis wind turbines.